If you enjoy riding a bike, then using it as your regular exercise will most likely bring you benefit with managing your COPD.
I've looked for one good UK article, but they are either too detailed, or too skimpy with their findings, so I've linked below to two summaries (one UK, one US, both reputable sources) that may be of interest:
https://www.blf.org.uk/support-for-you/copd/managing-my-copd
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4818249/
If you get offered a place on a Pulmonary Rehab course - take it. Not everyone does, but the info you'll pickup from the various healthcare professionals who run them can be really useful.
+1 for the importance of getting the right inhaler (there are many different inhalers, some contain the same type of drug)
AND being able to use it properly (they all work, but some are easier to get the right technique with than others).